On the stochastic response regimes of a tristable viscoelastic isolation system under delayed feedback control
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the stochastic response regimes of a tristable viscoelastic isolation system under delayed feedback control 1,2
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HUANG DongMei , ZHOU ShengXi , LI Wei & LITAK Grzegorz 1
School of Mathematics and Statistics, Xidian University, Xi’an 710071, China; School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China; Department of Automation, Lublin University of Technology, Lublin PL-20-618, Poland
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Received July 13, 2020; accepted September 9, 2020; published online October 27, 2020
In this paper, a tristable viscoelastic isolation system with stochastic excitation under both displacement and velocity delayed feedback control is considered. Firstly, the theoretical expressions of the mean first-passage time (MFPT) to measure the activated escape between different potential wells are derived. Induced nonlinear transition dynamics due to the noise and time delays are mainly discussed. It is found that the delay-induced behaviours affect the transitions between the equilibrium points of the system, the corresponding phenomenon of the delay-enhanced stability is observed. In this respect, the existence of the maxima of the MFPT1 and the MFPT2 is found in one period. Meanwhile, the MFPT1 and the MFPT2 show the monotonic behaviour with the increase of the noise intensity. Additionally, the stationary probability density of the amplitude and the stationary mean amplitude are derived. The influence regimes of the system parameters on both stationary probability density of the amplitude and the stationary mean amplitude are explored. This paper establishes the relationship between system parameters and dynamical properties of the tristable viscoelastic isolation system. This provides a fundamental guidance for the optimization of the viscoelastic isolation by utilizing the technique of delayed feedback control. stochastic excitation, time delay, viscoelastic isolation system, dynamical response Citation:
Huang D M, Zhou S X, Li W, et al. On the stochastic response regimes of a tristable viscoelastic isolation system under delayed feedback control. Sci China Tech Sci, 2020, 60, https://doi.org/10.1007/s11431-020-1724-x
1 Introduction In the field of the mechanical, aerospace and biological engineering, numerous time-delayed deterministic systems are frequently encountered in real applications. They have been extensively explored in many structures or systems [1–3], such as the neural networks [4–6], isolators or absorbers [7,8], biological systems [9–12], communication systems, etc. As one particular type of physical phenomena, time delays [2,13–15] are always inevitable due to the time taken on the transport of matter, energy, electrical fields and information through the system [14–19], etc. Additionally, time delays can be accumulated between interconnected *Corresponding author (email: [email protected])
systems [20–23]. On one hand, it is found that the existence of time delays in the systems not only causes the transfer properties to be changed, but also gives rise to the instabil
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